Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

1998/07/24 by Olga Perkovic, Olga Perković, Karin A. Dahmen +1 · 10 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech #nanoparticles nucleation surface interactions

paper · pdf · doi:10.1103/physrevb.59.6106

Condensed and updated version of cond-mat/9609072,``Disorder-Induced Critical Phenomena in Hysteresis: A Numerical Scaling Analysis''

arxiv created 1998/07/24 · openalex publication_date 1999/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an \ensuremathε expansion about six dimensions. We present the results of simulations in three, four, and five dimensions, with systems with up to a billion spins (1000³).

Citations

• Lectures on Phase Transitions and the Renormalization Group
• The renormalization group and the ε expansion
• Statistical characterization of Barkhausen noise
• Theory of dynamic critical phenomena
• Hysteresis Loop Critical Exponents in 6-Epsilon Dimensions
• Statistical Mechanics of Phase Transitions

Cited by

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• Local mean-field study of capillary condensation in silica aerogels
• Tailoring symmetry groups using external alternate fields
• Crackling noise, power spectra, and disorder-induced critical scaling
• Low-field hysteresis in disordered ferromagnets
• Microscopic foundations of the Rayleigh law of hysteresis
• Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the Renormalization Group
• Multifractal structure of Barkhausen noise: A signature of collective dynamics at hysteresis loop
• Critical hysteresis from random anisotropy
• Analysis of power-law exponents by maximum-likelihood maps